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m408dpracfin

# m408dpracfin - Math 408D Practice Final 1 Evaluate lim...

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Math 408D Practice Final 1. Evaluate lim x 0 sin(2 x ) x . 2. Evaluate Z 1 2 (4 x + 3) 2 dx. 3. Does the sequence ln( n 2 ) n converge? If so, to what? 4. Find X n =3 4 n ( n + 2) . 5. Tell whether X n =2 1 n 3 - n converges absolutely, converges conditionally or diverges. 6. Find the radius and interval of convergence of X n =1 ( n + 1) x 2 n - 1 3 n . 7. Find the first 4 non-zero terms of the Taylor series for f ( x ) = 50 - x around x = 1. 8. Use the first 4 non-zero terms of a Maclauren series to approximate Z 1 0 e - x 2 dx . 9. For the parametric curve x = e 2 t - t/ 2, y = e t , 0 t ln 2, (a) sketch the curve, and (b) find the equation of the line tangent to the curve at the point where t = 1. 10. Find the area inside r = 2 + 2 sin θ and outside r = 2. 11. Find the equation of the plane passing through the points (1 , - 1 , 2), (2 , 1 , 3), and ( - 1 , 2 , - 1). 12. Find the angle between the vectors a = 2 i + j - 4 k and b = - 3 i + 2 j + k . 13. Sketch a good graph of 4 y 2 + z 2 - 4 x 2 = 4.

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m408dpracfin - Math 408D Practice Final 1 Evaluate lim...

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